A car moving with a velocity of 20 ms^-1 stopped at a distance of 40 m. If the same car is travelling at double the velocity, the distance travelled by it for same retardation is

• 320 m

• 1280 m

• 160 m

• 640 m

A substance of mass 49.53 g occupies 1.5 cm³ of volume. The density of the substance (in g cm^-3) with correct number of significant figures is

• 3.3

• 3300

• 3302

• 33.0

Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air

• is equal to g (acceleration due to gravity)

• depends on the speeds of the two balls

• depends on the masses of the two balls

• depends on the direction of motion of the two balls

A body of the mass 50 kg is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, the reading of the spring balance is

• < 50 kg

• = 50 kg

• > 50 kg

• = 0

The S.I. unit of specific heat capacity is

• JK^-1

• J kg^-1

• J mol^-1 K^-1

• J kg^-1 K^-1

The value of acceleration due to gravity at a depth of 1600 km is equal to

• 4.9 ms^-2

• 9.8 ms^-2

• 7.35 ms^-2

• 19.6 ms^-2

7.

A motor pump lifts 6 tonnes of water from a well of depth 25 m to the first floor of height 35 m from the ground floor in 20 minutes. The power of the pump (in kW) is [g = 10 ms^-2]

• 3

• 12

• 15

• 6

If $\mathrm{A} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 8\hat{\mathrm{k}}$ is perpendicular to $\mathrm{B} = 4\hat{\mathrm{j}} - 4\hat{\mathrm{i}} + \mathrm{\alpha }\hat{\mathrm{k}}$, then the value of α is

• $- \frac{1}{2}$

• $\frac{1}{2}$

• 1

• − 1

The angle between velocity and acceleration of a particle describing uniform circular motion is

• 180°

• 90°

• 45°

• 60°

For which combination of working temperatures, the efficiency of engine is the least ?

• 100 K, 80 K

• 40 K, 20 K

• 80 K, 60 K

• 60 K, 40 K